Abstract
Let the soluble-by-finite group G=AB=AC=BC be the product of two nilpotent subgroups A and B and a subgroup C. It is shown that, if G has finite abelian section rank and C is hypercentral (hypercyclic), then G is hypercentral (hypercyclic). Moreover, if G is an L 1-group and C is nilpotent, then G is nilpotent.
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